14x+8x=2/3x

Solution for 14x+8x=2/3x equation:

14x+8x=2/3x

We move all terms to the left:

14x+8x-(2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

14x+8x-(+2/3x)=0

We add all the numbers together, and all the variables

22x-(+2/3x)=0

We get rid of parentheses

22x-2/3x=0

We multiply all the terms by the denominator


22x*3x-2=0

Wy multiply elements

66x^2-2=0

a = 66; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·66·(-2)
Δ = 528
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{33}}{2*66}=\frac{0-4\sqrt{33}}{132}
=-\frac{4\sqrt{33}}{132}
=-\frac{\sqrt{33}}{33}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{33}}{2*66}=\frac{0+4\sqrt{33}}{132}
=\frac{4\sqrt{33}}{132}
=\frac{\sqrt{33}}{33}
$